4,620 research outputs found

    Modeling multivariate financial time series based on correlation clustering.

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    Zhou, Tu.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 61-70).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.0Chapter 1.1 --- Motivation and Objective --- p.0Chapter 1.2 --- Major Contribution --- p.2Chapter 1.3 --- Thesis Organization --- p.4Chapter 2 --- Measurement of Relationship between financial time series --- p.5Chapter ´ب2.1 --- Linear Correlation --- p.5Chapter 2.1.1 --- Pearson Correlation Coefficient --- p.6Chapter 2.1.2 --- Rank Correlation --- p.6Chapter 2.2 --- Mutual Information --- p.7Chapter 2.2.1 --- Approaches of Mutual Information Estimation --- p.10Chapter 2.3 --- Copula --- p.12Chapter 2.4 --- Analysis from Experimental Data --- p.14Chapter 2.4.1 --- Experiment 1: Nonlinearity --- p.14Chapter 2.4.2 --- Experiment 2: Sensitivity of Outliers --- p.16Chapter 2.4.3 --- Experiment 3: Transformation Invariance --- p.20Chapter 2.5 --- Chapter Summary --- p.23Chapter 3 --- Clustered Dynamic Conditional Correlation Model --- p.26Chapter 3.1 --- Background Review --- p.26Chapter 3.1.1 --- GARCH Model --- p.26Chapter 3.1.2 --- Multivariate GARCH model --- p.29Chapter 3.2 --- DCC Multivariate GARCH Models --- p.31Chapter 3.2.1 --- DCC GARCH Model --- p.31Chapter 3.2.2 --- Generalized DCC GARCH Model --- p.32Chapter 3.2.3 --- Block-DCC GARCH Model --- p.32Chapter 3.3 --- Clustered DCC GARCH Model --- p.34Chapter 3.3.1 --- Minimum Distance Estimation (MDE) --- p.36Chapter 3.3.2 --- Clustered DCC (CDCC) based on MDE --- p.37Chapter 3.4 --- Clustering Method Selection --- p.40Chapter 3.5 --- Model Estimation and Testing Method --- p.42Chapter 3.5.1 --- Maximum Likelihood Estimation --- p.42Chapter 3.5.2 --- Box-Pierce Statistic Test --- p.44Chapter 3.6 --- Chapter Summary --- p.44Chapter 4 --- Experimental Result and Applications on CDCC --- p.46Chapter 4.1 --- Model Comparison and Analysis --- p.46Chapter 4.2 --- Portfolio Selection Application --- p.50Chapter 4.3 --- Value at Risk Application --- p.52Chapter 4.4 --- Chapter Summary --- p.55Chapter 5 --- Conclusion --- p.57Bibliography --- p.6

    Penalized Sieve Estimation and Inference of Semi-Nonparametric Dynamic Models: A Selective Review

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    In this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plug-in PSE estimators of functionals that are either smooth (i.e., root-n estimable) or non-smooth (i.e., slower than root-n estimable); (3) simple criterion-based inference for plug-in PSE estimation of smooth or non-smooth functionals; and (4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH, and copula-based multivariate financial models are used to illustrate the general results.Nonlinear time series, Temporal dependence, Tail dependence, Penalized sieve M estimation, Penalized sieve minimum distance, Semiparametric two-step, Nonlinear ill-posed inverse, Mixtures, Conditional moment restrictions, Nonparametric endogeneity, Dynamic asset pricing, Varying coefficient VAR, GARCH, Copulas, Value-at-risk

    The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey

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    This paper provides a selected review of the recent developments and applications of mixtures of normal (MN) distribution models in empirical finance. Once attractive property of the MN model is that it is flexible enough to accommodate various shapes of continuous distributions, and able to capture leptokurtic, skewed and multimodal characteristics of financial time series data. In addition, the MN-based analysis fits well with the related regime-switching literature. The survey is conducted under two broad themes: (1) minimum-distance estimation methods, and (2) financial modeling and its applications.Mixtures of Normal, Maximum Likelihood, Moment Generating Function, Characteristic Function, Switching Regression Model, (G) ARCH Model, Stochastic Volatility Model, Autoregressive Conditional Duration Model, Stochastic Duration Model, Value at Risk.

    Multivariate GARCH estimation via a Bregman-proximal trust-region method

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    The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parameters are subjected to convoluted nonlinear constraints necessary to ensure, for instance, the existence of stationary solutions and the positive semidefinite character of the conditional covariance matrices used in the model design. So far, this problem has been addressed in the literature only in low dimensional cases with strong parsimony constraints. In this paper we propose a general formulation of the estimation problem in any dimension and develop a Bregman-proximal trust-region method for its solution. The Bregman-proximal approach allows us to handle the constraints in a very efficient and natural way by staying in the primal space and the Trust-Region mechanism stabilizes and speeds up the scheme. Preliminary computational experiments are presented and confirm the very good performances of the proposed approach.Comment: 35 pages, 5 figure

    An Empirical Characteristic Function Approach to VaR under a Mixture of Normal Distribution with Time-Varying Volatility

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    This paper considers Value at Risk measures constructed under a discrete mixture of normal distribution on the innovations with time-varying volatility, or MN-GARCH, model. We adopt an approach based on the continuous empirical characteristic function to estimate the param eters of the model using several daily foreign exchange rates' return data. This approach has several advantages as a method for estimating the MN-GARCH model. In particular, under certain weighting measures, a closed form objective distance function for estimation is obtained. This reduces the computational burden considerably. In addition, the characteristic function, unlike its likelihood function counterpart, is always uniformly bounded over parameter space due to the Fourier transformation. To evaluate the VaR estimates obtained from alternative specifications, we construct several measures, such as the number of violations, the average size of violations, the sum square of violations and the expected size of violations. Based on these measures, we find that the VaR measures obtained from the MN-GARCH model outperform those obtained from other competing models.Value at Risk; Mixture of Normals; GARCH; Characteristic Function.

    Classifying the Markets Volatility with ARMA Distance Measures

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    The financial time series are often characterized by similar volatility structures. The selection of series having a similar behavior could be important for the analysis of the transmission mechanisms of volatility and to forecast the time series, using the series with more similar structure. In this paper a metrics is developed in order to measure the distance between two GARCH models, extending well known results developed for the ARMA models. The statistic used to calculate it follows known distributions, so that it can be adopted as a test procedure. These tools can be used to develope an agglomerative algorithm in order to detect clusters of homogeneous series.GARCH models, clusters, agglomerative algorithm
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